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question_answer1)
The area of the closed figure bounded by \[x=-1,\]\[y=0,\] \[y={{x}^{2}}+x+1\], and the tangent to the curve \[y={{x}^{2}}+x+1\] at A(1,3) is
A)
4/3 sq. units done
clear
B)
7/3 sq. units done
clear
C)
7/6 sq. units done
clear
D)
None of these done
clear
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question_answer2)
The area of the closed figure bounded \[y=\frac{{{x}^{2}}}{2}-2x+2\] and the tangents to it at (1, 1/2) and (4, 2) is
A)
9/8 sq. units done
clear
B)
3/8 sq. units done
clear
C)
3/2 sq. units done
clear
D)
9/4 sq. units done
clear
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question_answer3)
The area bounded by the two branches of curve \[{{(y-x)}^{2}}={{x}^{3}}\] and the straight line x = 1 is
A)
1/5 sq. units done
clear
B)
3/5 sq. units done
clear
C)
4/5 sq. units done
clear
D)
8/4 sq. units done
clear
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question_answer4)
The area of the region bounded by \[{{x}^{2}}+{{y}^{2}}-2x-3=0\] and \[y=\left| x \right|+1\]is
A)
\[\frac{\pi }{2}-1\] sq. units done
clear
B)
\[2\pi \]sq. units done
clear
C)
\[4\pi \]sq. units done
clear
D)
\[\pi /2\]sq. units done
clear
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question_answer5)
The area of the loop of the curve \[a{{y}^{2}}={{x}^{2}}(a-x)\] is
A)
\[4{{a}^{2}}\]sq. units done
clear
B)
\[\frac{8{{a}^{2}}}{15}\]sq. units done
clear
C)
\[\frac{16{{a}^{2}}}{9}\]sq. units done
clear
D)
None of these done
clear
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question_answer6)
The area of the figure bounded by the parabola \[{{(y-2)}^{2}}=x-1\], the tangent to it at the point with the ordinate x = 3, and the x-axis is
A)
7 sq. units done
clear
B)
6 sq. units done
clear
C)
9 sq. units done
clear
D)
None of these done
clear
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question_answer7)
The area enclosed by the curve \[y=\sqrt{4-{{x}^{2}}},\] \[y\ge \sqrt{2}\sin \left( \frac{x\pi }{2\sqrt{2}} \right)\], and the x-axis is divided by the y-axis in the ratio
A)
\[\frac{{{\pi }^{2}}-8}{{{\pi }^{2}}+8}\] done
clear
B)
\[\frac{{{\pi }^{2}}-4}{{{\pi }^{2}}+4}\] done
clear
C)
\[\frac{\pi -4}{\pi -4}\] done
clear
D)
\[\frac{2{{\pi }^{2}}}{2\pi +{{\pi }^{2}}-8}\] done
clear
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question_answer8)
Let\[f(x)={{x}^{3}}+3x+2\] and g(x) be the inverse of it. Then the area bounded by g(x), the x-axis, and the ordinate at \[x=-\,2\] and \[x=6\] is
A)
1/4 sq. units done
clear
B)
4/3 sq. units done
clear
C)
5/4 sq. units done
clear
D)
7/3 sq. units done
clear
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question_answer9)
The area bounded by the x-axis, the curve \[y=f(x)\], and the lines x = 1, x = b is equal to\[\sqrt{{{b}^{2}}+1}-\sqrt{2}\] for all b > l, then f(x) is
A)
\[\sqrt{x-1}\] done
clear
B)
\[\sqrt{x+1}\] done
clear
C)
\[\sqrt{{{x}^{2}}+1}\] done
clear
D)
\[\frac{x}{\sqrt{1+{{x}^{2}}}}\] done
clear
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question_answer10)
The area enclosed between the curve \[{{y}^{2}}(2a-x)={{x}^{3}}\] and the line x = 2 above the x-axis is
A)
\[\pi {{a}^{2}}\]sq. units done
clear
B)
\[\frac{3\pi \,{{a}^{2}}}{2}\] sq. units done
clear
C)
\[2\pi \,{{a}^{2}}\]sq. units done
clear
D)
\[3\pi \,{{a}^{2}}\] sq. units done
clear
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question_answer11)
Consider two curves \[{{C}_{1}}:{{y}^{2}}=4[\sqrt{y}]x\] and\[{{C}_{2}}:{{x}^{2}}=4[\sqrt{x}]y\], where [.] denotes the greatest integer function. Then the area of region enclosed by these two curves within the square formed by the lines x =1, y =1, x = 4, y = 4 is
A)
8/3 sq. units done
clear
B)
10/3 sq. units done
clear
C)
11/3 sq. units done
clear
D)
11/4 sq. units done
clear
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question_answer12)
The area bounded by the curve y = x \[\left| x \right|\], x-axis and the ordinates x = 1, \[x=-1\] is given by
A)
0 done
clear
B)
1/3 done
clear
C)
2/3 done
clear
D)
None of these done
clear
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question_answer13)
Area lying in the first quadrant and bounded by the curve \[y={{x}^{3}}\] and the line y = 4x is
A)
2 done
clear
B)
3 done
clear
C)
4 done
clear
D)
5 done
clear
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question_answer14)
The area bounded by the curves \[x={{y}^{2}}\] and \[x=\frac{2}{1+{{y}^{2}}}\] is
A)
\[\pi -\frac{2}{3}\] done
clear
B)
\[\pi +\frac{2}{3}\] done
clear
C)
\[-\pi -\frac{2}{3}\] done
clear
D)
none of these done
clear
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question_answer15)
The area bounded by the curve y = sin x and the line x = 0, \[\left| y \right|=\frac{\pi }{2}\] is
A)
1 done
clear
B)
2 done
clear
C)
\[\pi \] done
clear
D)
2\[\pi \] done
clear
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question_answer16)
The area of the region in 1st quadrant bounded by the y-axis, y = \[\frac{x}{4}\], y = 1 + \[\sqrt{x}\], and \[y=\frac{2}{\sqrt{x}}\] is
A)
2/3 sq. units done
clear
B)
8/3 sq. units done
clear
C)
11/3 sq. units done
clear
D)
13/6 sq. units done
clear
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question_answer17)
The area enclosed by the curves \[y=\text{sin}\,x+\text{cos}\,x\]and \[y=\left| \text{cos }x-\text{sin }x \right|\] over the interval [0,\[\pi /2\]] is
A)
\[4(\sqrt{2}-1)\] done
clear
B)
\[2\sqrt{2}(\sqrt{2}-1)\] done
clear
C)
\[2(\sqrt{2}+1)\] done
clear
D)
\[2\sqrt{2}(\sqrt{2}+1)\] done
clear
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question_answer18)
The area enclosed by \[y={{x}^{2}}+\cos x\] and its normal at \[x=\frac{\pi }{2}\] in the first quadrant is
A)
\[\frac{{{\pi }^{5}}}{32}-\frac{{{\pi }^{4}}}{64}+\frac{{{\pi }^{3}}}{32}+1\] done
clear
B)
\[\frac{{{\pi }^{5}}}{16}-\frac{{{\pi }^{4}}}{32}+\frac{{{\pi }^{3}}}{24}-1\] done
clear
C)
\[\frac{{{\pi }^{5}}}{32}-\frac{{{\pi }^{4}}}{32}+\frac{{{\pi }^{3}}}{16}\] done
clear
D)
\[\frac{{{\pi }^{5}}}{32}-\frac{{{\pi }^{4}}}{32}+\frac{{{\pi }^{3}}}{24}+1\] done
clear
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question_answer19)
The area enclosed between the curves \[y=a{{x}^{2}}\] and \[x=a{{y}^{2}}\] (where a > 0) is 1 sq. unit, then the value of a is
A)
\[1/\sqrt{3}\] done
clear
B)
½ done
clear
C)
1 done
clear
D)
1/3 done
clear
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question_answer20)
The area bounded by the curve \[{{y}^{2}}(2-x)={{x}^{3}}\] and x = 2 is
A)
\[\frac{\pi }{2}\] done
clear
B)
\[\pi \] done
clear
C)
\[2\pi \] done
clear
D)
\[3\pi \] done
clear
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question_answer21)
The area bounded by the curves \[y={{\log }_{e}}x,\,\,y={{\log }_{e}}\left| x \right|,\]\[y=\left| {{\log }_{e}}x \right|,\]and \[y=\left| {{\log }_{e}}\left| x \right| \right|\] is ____.
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question_answer22)
The area of the region bounded by the curves \[y=\left| x-2 \right|,\] x=1, x=3, and the x-axis is ____.
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question_answer23)
The area enclosed between the curve \[y={{\log }_{e}}(x+e)\] and the coordinate axes is ____.
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question_answer24)
The area of the region bounded by the curves \[y=\left| x-1 \right|\] and \[y=3-\left| x \right|\] is ____.
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question_answer25)
The area of the plane region bounded by the curves \[x+2{{y}^{2}}=0\] and \[x+3{{y}^{2}}=1\] is equal to _______.
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